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Rotating magnetic field effect on convection and its stability in a horizontal cylinder subjected to a longitudinal temperature gradient

Published online by Cambridge University Press:  15 October 2010

D. V. LYUBIMOV ,
A. V. BURNYSHEVA ,
H. BENHADID ,
T. P. LYUBIMOVA  and
D. HENRY
D. V. LYUBIMOV
Affiliation:
Perm State University, 15 Bukirev Street, 614990 Perm, Russia
A. V. BURNYSHEVA
Affiliation:
Institute of Continuous Media Mechanics UB RAS, 1 Koroleva Street, 614013 Perm, Russia
H. BENHADID
Affiliation:
Laboratoire de Mécanique des Fluides et d'Acoustique, Université de Lyon, École Centrale de Lyon, Université Lyon 1, INSA de Lyon, UMR-CNRS 5509, 43 Bd du 11 Novembre 1918, 69622 Villeurbanne CEDEX, France
T. P. LYUBIMOVA
Affiliation:
Institute of Continuous Media Mechanics UB RAS, 1 Koroleva Street, 614013 Perm, Russia
D. HENRY*
Affiliation:
Laboratoire de Mécanique des Fluides et d'Acoustique, Université de Lyon, École Centrale de Lyon, Université Lyon 1, INSA de Lyon, UMR-CNRS 5509, 43 Bd du 11 Novembre 1918, 69622 Villeurbanne CEDEX, France
*
†Email address for correspondence: daniel.henry@ec-lyon.fr
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Abstract

A rotating magnetic field (RMF) is used in crystal growth applications during the solidification process in order to improve the crystal quality. Its influence on the convective flows in molten metals and on their stability is studied here in the case of a horizontal infinite cylindrical channel subjected to a longitudinal temperature gradient. The steady convective flows, which correspond to the usual longitudinal counterflow structure, with four vortices in the cross-section for non-zero Prandtl number, Pr, are modified by the RMF (parametrized by the magnetic Taylor number Tam). For zero Prandtl number, the flow in the cross-section corresponds to circular streamlines and the longitudinal flow structure is moved in the direction of the magnetic field rotation, with a decrease in its intensity and an asymptotic variation as 1/Tam. For non-zero Prandtl numbers, depending on the respective values of Tam on one side and Prandtl and Grashof numbers on the other side, different structures ranging from the circular streamlines with transport by rotation of the longitudinal velocity and the temperature field, to the more usual counterflow structure almost insensitive to the RMF with four cross-section vortices, can be obtained. The decrease in the flow intensity with increasing Tam is also delayed for non-zero Pr, but the same asymptotic limit is eventually reached. The stability analysis of these convective flows for Tam = 0 shows a steep increase of the thresholds around Pr = Prt,0 ≈ 3 × 10−4, corresponding to the transition between the usual counterflow shear mode and a new sidewall shear mode. This transition is still present with an RMF, but it occurs for smaller Pr values as Tam is increased. Strong stabilizing effects of the rotating magnetic field are found for Pr < Prt,0, particularly for Pr = 0 where an exponential increase of the threshold with Tam is found. For Pr > Prt,0 (i.e. in the domain where the sidewall instability is dominant), in contrast, the stabilization by the RMF is weak.

JFM classification

Convection: Convection in cavities Instability: Instability
Type
Papers
Information
Journal of Fluid Mechanics , Volume 664 , 10 December 2010 , pp. 108 - 137
Copyright
Copyright © Cambridge University Press 2010

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